On the hyperkähler metrics associated to singularities of nilpotent varieties
type: Item
instance of: scholarly article
title: On the hyperkähler metrics associated to singularities of nilpotent varieties
zbMATH Open document ID: 0874.53036
DOI: 10.1007/BF00127972
author: Roger Bielawski
published in: Annals of Global Analysis and Geometry
publication date: 1996-08-28T00:00:00Z
review text: Let \(G\) be a complex, semisimple Lie group, and \(N\) the nilpotent variety in the Lie algebra of \(G\). The hyperkähler metrics associated to minimal singularities in the nilnotent variety are studied in this paper. Kronheimer's 4-dimensional ALE (Asymptotically Locally Euclidean) spaces are naturally realized within the context of coadjoint orbits and are identified as certain moduli spaces of SU(2)-invariant instantons on \(\mathbb{R}^k\setminus\{0\}\) with appropriate boundary conditions. The author also shows that the hyperkähler metrics on the resolution of the \(D_2\) singularity arise within coadjoint orbits. The author further gives the description of the hyperkähler metric on the orbit of highest root vectors.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14L40
zbMATH DE Number: 895829
zbMATH Keywords: hyperkähler metrics
zbMATH Keywords: nilnotent variety
zbMATH Keywords: coadjoint orbits
reviewed by: V. Lakshmibai
MaRDI profile type: Publication
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Wikidata QID: Q125767159
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description: scientific article; zbMATH DE number 895829